I have to handle a class of symbolic integral with the form, more precisely,
When I set $u(x,t) = e^{-t}x^2(1-x)^2$, then how to compute \begin{equation} I = \frac{1}{\Gamma(1-\alpha)}\int^{t}_0\frac{\partial u(x,\eta)}{\partial \eta}\frac{d\eta}{(t - \eta)^{\alpha}} \end{equation} and if we set $u(x,t) = \sin(t+1)x^3(1-x)^3$, again, how to compute $I$, are there some tips for handling this kind of symbolic integral ?